PRODUCT OF MAGNETIC ENERGIES. 21 



will deflect the needles mounted on the axis. As every 

 one of the actions between the respective poles is a 

 statical action, and as the mean of the actions on the 

 nearer pole and the further pole of the needle will be 

 sensibly the same as if each was at the needle's center, 

 the trigonometrical tangent of deflection will be the 

 proportion of the statical force exerted by the magnet 

 to the statical force exerted by the Earth. Now the 

 fact of experiment is, that the deflection produced by 

 the external magnet in the assemblage of needles is 

 exactly the same as the deflection produced in a single 

 needle. And therefore the proportion of the statical 

 force exerted by the external magnet to the statical 

 force exerted by the Earth is the same in both cases. 

 But, as we have seen, the statical force exerted by the 

 Earth is proportioned to the number of needles or to 

 the sum of magnetic energies of the needles ; and 

 therefore the statical force exerted by the external 

 magnet is proportional to the sum of magnetic energies 

 of the needles. And the algebraical expression for 

 that statical force must contain that sum of magnetic 

 energies of the disturbed needles as factor. The same 

 rule holds good with regard to gravitation. 



It may at first appear strange that the pull exerted 

 by a magnet upon several needles is greater than the 

 pull exerted upon a single needle, and that in fact a 

 new equal pull is ready to act upon every new equal 

 needle exposed to it. But the fact is so; and it is ana- 

 logous to the gravitation-attraction exercised by a 

 planet upon several satellites, in which the force upon 



